The movie character/minifig should be M'Baku. The Man-Ape name comes from his character in the comics. In the comics, he actually wears a white gorilla themed costume, and has powers derived from a mystical white gorilla.
Unlikely, since they are competing toy brands. Hot Wheels is owned by Mattel, which also owns Mega Bloks. That is why the buildable Hot Wheels sets also have the "Mega" logo on them.
You sir, have a LOT of patience. As an adult Lego fan and a parent I always try to remember that many of this wiki's users are on the younger side, but I don't think I could ever do what you do. Huge props to you.
For licensed sets, Lego is typically given advanced knowledge (concept art, etc) of items before they are released, so as to be able to have sets designed, manufactured, and ready to sell before things (shows, games, etc.) go live. Depending in the IP and licensing agreements/contracts, this can (and has several times) resulted in the release of sets well before the things/characters/scenes they are depicting "come out."
So not really a prediction. If anything, Mojang probably told Lego it was going to be a thing, and Lego made the set, then Mojang pushed back their internal schedule and delayed actually adding it to the game, causing the set to be released well before the game update.
Not directly, but they are both owned by Mattel. They used to be competitors, but now have the same parent company.
Hot Wheels is owned by Mattel, which also owns Mega Blocks. I'll now give you one guess as to why you'll never see a Lego / Hot Wheels collaboration...